Abstract

We explore the concept of seniority number (defined as the number of unpaired electrons in a determinant) when applied to the problem of electroncorrelation in atomic and molecular systems. Although seniority is a good quantum number only for certain model Hamiltonians (such as the pairing Hamiltonian), we show that it provides a useful partitioning of the electronic full configuration interaction (FCI) wave function into rapidly convergent Hilbert subspaces whose weight diminishes as its seniority number increases. The primary focus of this study is the adequate description of static correlation effects. The examples considered are the ground states of the helium, beryllium, and neon atoms, the symmetric dissociation of the N2 and CO2 molecules, as well as the symmetric dissociation of an H8 hydrogen chain. It is found that the symmetry constraints that are normally placed on the spatial orbitals greatly affect the convergence rate of the FCI expansion. The energy relevance of the seniority zero sector (determinants with all paired electrons) increases dramatically if orbitals of broken spatial symmetry (as those commonly used for Hubbard Hamiltonian studies) are allowed in the wave function construction.

The authors thank Jorge Dukelsky and Dr. Chris Diaconu for useful discussions. This work was supported by the Department of Energy (DOE) (Grant No. DE-FG02-09ER16053) and The Welch Foundation (C-0036). L.B. gratefully acknowledges the computational resources at Ames Laboratory U.S. DOE.